Near round number squared

Have you ever had a problem like 81², or 31², or maybe even 69²? How are you supposed to do it?

To explain, we’ll use 81 x 81. Remember that 81 is really close to 80 and 80 x 80 = 6400. So 80 x 81 = 6400 + 80 = 6480. 81 x 81 = 6480 + 81 = 6561

Let’s look at it with a smaller example, 21 x 21 to better understand.

All of the red blocks together is 20 x 20 (400), but the thing is we want 21 x 21 so what do we do? We add the 20 light blue boxes to make the height 21 but we also want the width to be 21 so we add an extra 21 blue boxes to make it a 21 x 21 . So what we added is a 20 and a 21 to 400 and we get 20 + 21 + 400 = 441.

So to generalize, if you know n², then to find (n+1)², you add n to n² and then add n+1.

The same can be done for (n-1)² also. First you take away a n and then you take away n-1 from n².

Easy!